<h2>题目编号 : 286</h2>
<div style="color:#666;font-size:80%;">03 April 2010</div><br />
<div class="problem_content">
<p>Barbara is a mathematician and a basketball player. She has found that the probability of scoring a point when shooting from a distance <var>x</var> is exactly (1&thinsp;-&nbsp;<img src="" style="display:none;" alt="^(" /><sup><var>x</var></sup><img src="" style="display:none;" alt=")" />/<img src="" style="display:none;" alt="_(" /><sub><var>q</var></sub><img src="" style="display:none;" alt=")" />), where <var>q</var> is a real constant greater than 50.</p>

<p>During each practice run, she takes shots from distances <var>x</var>&thinsp;=&thinsp;1, <var>x</var>&thinsp;=&thinsp;2, ..., <var>x</var>&thinsp;=&thinsp;50 and, according to her records, she has precisely a 2&thinsp;% chance to score a total of exactly 20 points.</p>

<p>Find <var>q</var> and give your answer rounded to 10 decimal places.</p>
</div><br />
